## The Omega Unit

Introducing the concept of a Tetryonic 'integer' unit.

Connecting the dots between Wayne Roberts Scale Structure Theory to that of Tetryonics 'Square Numbers' in Physics, I hope to show that this new way of looking at the universe is valid and expressive in ways we need to recognize and appreciate. The future is here, right now, and we are the ones we've been waiting for.

"What exactly is a unit? And, by implication, a number? And how might these abstract concepts be best represented or symbolized within the jurisdiction of a language of which they form the parts? Is an 'intuitive knowing' (axiom) called for? A 'given' which must forever remain 'incompletely definable' (here alluding to Gödel's Incompleteness Theorem) because the concept of the unit lies at the heart of definitions themselves, and therefore any definition of itself must surely, ipso facto, be tautologous? We must remember that all things in our Universe (including 'definitions') are relative as required by the Principle of Universal Relativity —nothing is 'cut off' or separated, else it remains unknowable, neither may it 'influence' or 'be influenced'.

There seems little doubt we are on the threshold of a rich new expressive means in the arts and of powerful new theories in science. The adoption and further exploration of the principles outlined below may lead to the development of a highly sophisticated language—one that might be understood universally. This is because such a language would reflect universal organization in principle. Such a universal language could extend the potential for expression and communication far beyond what we currently know as art or language. The gradual elucidation of scale structures together with syntactical exploration and interconnection of these will result in the discovery of not only a powerful expressive means but also a high-order language with the ability to extend science and art, in fact thinking itself, to a level we might only dream of today.

The challenge for the new art is not only to discover resonant scale structures and syntaxes but to apply and combine these to form a new language of visual forms and events. The sign that we are on the right track in our quest will be that the new syntax and scale structures connect up in exquisite ways with many existing covert scale structures within mathematics, music, topology, linguistics, and the natural world. Ultimately, the new language will embrace them all. Then we shall know ourselves, each other, and the universe more fully.

This document is therefore but a beginning; an outline of the principles of new ways of thinking, creating, exploring. It presents a new frontier, a new challenge. My hope is that it advances not only the cause of art, but of how we think, and of what we can know. The theory stands upon the shoulders of many giants of the past, bringing together their history-making breakthroughs within a single schema. Thus the theory is both new and old. It is new in what it brings together and in how it is brought together. In addition, new concepts are proposed and these are then applied to the foundations of geometry and number theory including Pythagoras' theorem. But it is a newness that builds upon the foundation of the individual achievements of many others; a consciousness not only of human history, but of the human discovery of cosmic origins, timescales, and orders. Finally, the document presents a number of conjectures arising from the theory, and whether these are someday proven true or partly true is perhaps less important than whether the general premise of the ideas here presented proves to be valuable to peoples or persons now or in the future.

...A significant oversight and omission is thus revealed at the fundamental level of the notion of the unit in mathematics—at the very least, units pertaining to the measurement of areas - including the concept of units as taught in primary, secondary, and even (sometimes) tertiary education. [In light of the equally-triangular nature of the so-called 'square numbers']...is it not curious then, that in the history of mathematics, squares have served the role of 'general-purpose units-of-area', it would appear by default rather than design? We have applied square plugs to nearly every shaped hole under the mathematical sun. The notion of units-relative-to-wholes has not been taken up seriously perhaps because issues of comparison have tended to focus on differences more than similarities or 'resonances'. In the comparative measurement of areas, we have inducted the square as the default unit of area and a universal arbiter of comparison ('this area is so-many-square units whereas that area is a lesser number of equivalent square units, and is therefore smaller'). It is ironic because comparisons involve relating something to something else, and thus a choice of units relative to the system concerned must ultimately be simpler and more powerful. We have applied ‘square plugs’ to nearly every shaped hole under the mathematical sun....the application of relative units to mathematical and spatial problems allows a deeper understanding of qualitative differences as well as a simpler and more resonant connection of geometric problems to number theory and analysis. Thus every 'square' number can just as easily be represented in equilateral triangular form."

-- Wayne Roberts - via Scale Structure Theory

If not us, who? If not now, when?

"Every one of our laws is a purely mathematical statement using rather complex and abstruse mathematics. It's successes have fostered a tendency to forget that mathematics in NOT physics."--Abraham

We are looking at numbers from a Tetryonic perspective and connect these concepts to that of Scale Structure Theory (Wayne Roberts). We are attempting to highlight the notion that 'Square Numbers' are in fact Equilateral Triangular Geometries. The nature of Units is also called into question whereby a re-definition of the unit is necessary in order to advance our understanding of physical systems. Only when these concepts are accepted can we delve deeper into the erroneous assumptions made by the Standard Model, setting it on a path correction leading to unforeseen advances in many areas of study. By applying Equilateral Geometry to numbers, mass , Energy and Matter, a new level of understanding and a new road map for the future of science is offered.

Wayne Roberts suggests that these principles will assist to develop a new visual language leading to new ways to think about our universe. Tetryonics goes a step further and demonstrates that this is in fact true. By applying the notion of 'Square numbers' to Equilateral Triangular Geometries, Tetryonics offers a new visual language confidently resting upon the firm foundations of Geometry.

"If math is the language of Physics, then Geometry is the grammar that the math must follow."K.C.ABRAHAM

If you relate the concept of a numerical ‘Integer’ to that of a geometric energy ‘quantum’ you’ll find it's a better way of defining it as Tetryonics does in Quantum Mechanics Book One, concerning introductory math & throughout T[5] – Geometrics.

Best definition we can give is “Square numbers are in fact EQUILATERAL geometries.” This covers it all because squares are equilateral just as equilateral triangles are. In fact we’d love to just drop ‘square numbers’ from our vernacular but it is deeply ingrained [just like dodecahedrons being hexagonal etc.]. We take care to place quotes around 'square numbers' because English just isn't descriptive enough in this area, and the reference word, square, has lead us to looking at actual squares rather than realizing that the tessellation of Equilateral Geometries produce all the square numbers of physics.

Introducing the concept of a Tetryonic 'integer' unit.

The “Omega’ unit:

- The name and symbol reflect the equilateral geometry and EM field flux of all quanta

- Its foundational units would be Pi radians

- Combined with mass [Energy/sec] it gives Planck’s Constant [h] in physics

- Its geometry [m^2] per second reflects the unit of quantised angular momentum [QAM]

One ‘integer’ Omega unit is Pi radians and provides the geometric foundation for all of Physics.

The Tetryon forms the Matter quanta in physics, so we find it useful to keep everything in units of [pi] for Tetryonics. If someone was to work exclusively with EM photons [Light] no doubt it could be used to used to create an integer unit for that work [ie Photon = 2pi E] but again the results obtained would then have to be all converted back to [pi] geometries and formula so as to present their work in a base unit.

What we are trying to convey here is that 2pi [TAU] bases relate specifically to Photons – while there remains a need to express final results in terms of pi [Charge] or [4pi] Matter units for true equivalence throughout physics.

Using TAU & PI bases without a full understanding of the geometry will lead to a result similar to the Planck-Einstein one where it is often stated in textbooks that hv= E = hf . Mathematically that's the same as saying 2 =1, or Even = Odd and therefor must be corrected from this point forward, and all modern text books need to be re-written with that in mind.

While we support the premise of Tau, it too is short-sighted and fails when it comes to providing an appropriate base unit for Physics in general.

The following is the best summation of the geometric bases:

The Charged [ODD pi] geometry of 2-D [npi] mass – ENERGY [pi] - Matter [4npi]

It helps to maintain the units and equations reflective of the number of sides each particle and field has.

Specifically:

Bosons ODD pi 2D mass charge geometries

Photons EVEN pi 2D mass tau geometries

Tetryons 4pi 3D Matter Tetryonic geometry

Quarks-Lepton 12pi 3D Matter Dodecadeltahedron geometries

Mesons 24pi 3D Matter Dual -Dodecadeltahedron

Baryons 36pi 3D Matter Tri - Dodecadeltahedron

Elements 84pi 3D Matter Elemental

The [base] unit here is obviously [pi] geometries which are the radian geometries formed by QAM [OMEGA].

**To Be Continued....**